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Description: Although basing conclusions on confidence intervals for effect size estimates is preferred over relying on null hypothesis significance testing alone, confidence intervals in psychology are typically very wide. One reason may be a lack of easily applicable methods for planning studies to achieve sufficiently tight confidence intervals. This paper presents tables and freely accessible tools to facilitate planning studies for the desired accuracy in parameter estimation for a common effect size (Cohen’s d). In addition, the importance of such accuracy is demonstrated using data from the Reproducability Project: Psychology (RPP). It is shown that the sampling distribution of Cohen’s d is very wide unless sample sizes are considerably larger than what is common in psychology studies. This means that effect size estimates can vary substantially from sample to sample, even with perfect replications. The RPP replications’ confidence intervals for Cohen’s d have widths of around 1 standard deviation (95% confidence interval from 1 to 1.34). Therefore, point estimates obtained in replications are likely to vary substantially from the estimates from earlier studies. The implication is that researchers in psychology -and funders- will have to get used to conducting considerably larger studies if they are to build a strong evidence base.